The Toroidal Electron: A Unified Geometric Theory of Electromagnetic Structure, Mass, and the Fine Structure Constant

We present a comprehensive theoretical framework in which the electron is described as a topologically trapped electromagnetic field in a toroidal configuration, stabilized by Hopf fibration topology. This model provides a unified explanation for several fundamental electron properties: charge quantization emerges from the topological linking number, spin-½ arises naturally from the SU(2) ≅ S³ structure, and wave-particle duality is resolved through the electromagnetic near-field/far-field transition. Most significantly, we derive numerical formulas connecting fundamental constants to geometric structures. The fine structure constant is expressed as α = Z₀/(2RK), revealing it as an impedance ratio. The electron mass follows the relation me = mP × α^(21/2 - 15α/4), where the exponent 21 = 3 × 7 arises from the dimensions of the first two Hopf fibration total spaces (S³ and S⁷), and the correction term involves 15 = dim(SO(4,2)), the conformal group dimension. This formula achieves 0.008% accuracy. We demonstrate deep structural parallels with Wyler's geometric derivation of α, suggesting both constants emerge from the same underlying geometry involving Hopf fibrations, the conformal group, and exceptional symmetries. These results point toward a geometric unification of electromagnetism, quantum mechanics, and potentially gravity. Note: This is a working preprint. Updated versions may follow.